Reproductive value and the stochastic demography of age-structured populations.

The dynamics of an age-structured population in a fluctuating environment is determined by the stochastic individual contributions from annual survival and fecundity to the total reproductive value of the population the next year. All parameters required to describe the population dynamics are simple properties of the distribution of these individual demographic contributions, which we call individual reproductive value. The asymptotic population growth rate in the average environment and the demographic and environmental variances are respectively the mean individual reproductive value over individuals through time and the variance within and between years. Our approach leads to an intuitive understanding of demographic and environmental variances in age-structured populations and their decomposition into additive age-specific components due to survival and reproduction. We show how to apply this approach to estimate the demographic and environmental variances and their components. The estimates are based on yearly random samples of individual vital rates and require no information about the total population size.